منابع مشابه
G-linear sets and torsion points in definably compact groups
Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G \ X) < dimG for some definable X ⊆ G then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.
متن کاملDefinably compact abelian groups
Let M be an o–minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n–dimensional group definable in M. We show the following: the o–minimal fundamental group of G is isomorphic to Z; for each k > 0, the k–torsion subgroup of G is isomorphic to (Z/kZ), and the o–minimal cohomology algebra over Q of G is isomorphic to the exterior algebra over Q with ...
متن کاملO-minimal cohomology and definably compact definable groups
LetN an o-minimal expansion of a real closed field. We develop the cohomology theory for the category ofN -definable manifolds with continuous N -definable maps and use this to solve the Peterzil-Steinhorn problem [ps] on the existence of torsion points onN -definably compact N -definable abelian groups. Namely we prove the following result: Let G be an N -definably compact N -definably connect...
متن کاملDefinably connected nonconnected sets
We give an example of a structure K on the real line, and a manifold M definable in K, such that M is definably connected but is not connected.
متن کاملO-minimal cohomology with definably compact supports
We define here the o-minimal cohomology theory with definably compact supports and prove that this theory is invariant in elementary extensions, in o-minimal expansions and coincides with its topological analogue for o-minimal structures in the real numbers. As an application we show that on definably locally compact definable sets the o-minimal Euler characteristic coincides with the Euler-Poi...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2007
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm193-2-4